Rank Metric Codes and Their Galois Duality

Abstract

In this paper, we describe the Galois dual of rank metric codes in the ambient space FQn×m and FQmn, where Q=qe. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of qsm-dual bases of FQm over FQ and obtain some conditions about the existence of qsm-self-dual basis.